1. OK, I see. I have consulted with Dr, Karpov on the default parameters and electrical conductivity of n-GaN. He confirmed that they are quite OK, and correction (if any) will be of minor. However, he said that in highly-doped semiconductor another mechanism of conductivity may be important, which is related to carrier hopping from one impurity state to a neighbour one, with no creation of "free" carriers we account for. It is hard to calculate exactly impact of that mechanism, but the upper limit of the conductivity is sigma = electron_charge * donor_concentration * electron_mobility, which is equivalent to complete ionization of donors.

So, it may be reasonable to increase n-GaN conductivity 2-3 times. One can do it by increase of donor concentration, or by direct input of the conductivity, no matter.

2. The theta value in mobility photo is the compensation ratio, i.e. the ratio of the acceptor atoms to donor ones. If an acceptor atom is introduced into n-type semiconductor, it immediately catches one electron and exclude it from "free" electrons taking part in conductivity. So, the same electron concentration may be reached with different number of donors and acceptors. Below, let us assume complete donor ionization to simplify explanation. Then the electron concentration of, say, 2e18 can be created by 2e18 donors and no acceptors, or by 3e18 donors and 1e18 acceptors, and so on. However, each impurity atom contributes to the electron scattering, so at high compensation ratio the conductivity is lower even at the same electron concentration.

Please fins attached a screenshot from the Ioffe database with definition of theta used in this section.